Abstract
The layout of two-terminal nets in a VLSI channel is realized in a new diagonal channel-routing model (DCRM), where the tracks are segments respectively displayed at +45 ° and −45 ° on the two layers of the channel. A new definition of channel density is introduced, and a lower bound to the channel width is derived by the application of an algorithm, whose complexity is evaluated as a function of the channel density, and other parameters of the problem.
A simple linear-time algorithm is proposed, which produces an optimal layout (i.e., it requires a channel of minimum width) if the length of the longest net equals the lower bound for the channel width. In any case, the number of vias is at most one for each net. Some particular solutions are proposed for problems with long nets.
Specific problems are much easier in DCRM than in the classical Manhattan model. For example, any shift-by-i can be realized in DCRM in a channel of widthi.
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References
Hu, T. C., and Kuh, E. S., Theory and Concepts of Circuits Layout, in T. C. Hu and K. S. Kuh, eds.,VLSI Circuit Layout: Theory and Design, Selected Reprint Series, IEEE Press, New York, 1985.
Hightower, D., The Interconnection Problem: A Tutorial,Computer,7 (1974), 18–32.
Leighton, T., A Survey of Problems and Results for Channel Routing, A.W.O.C., Loutraki, July 1986.
Lipski, W., and Preparata, F. P., An Elementary Theory of Layout Wirability, Tech. Rep. ACT 54, Coordinated Science Laboratory, University of Illinois, 1985.
Sarrafzadeh, M., Hierarchical Approaches to VLSI Circuit Layout, Tech. Rep. ACT 72, Coordinated Science Laboratory, University of Illinois, 1986.
Szymansky, T. G., Dogleg Channel Routing is NP-Complete,IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems,4 (1985), 31–41.
Szymansky, T. G., and Yannakakis, M., Private communication.
Preparata, F. P., and Lipski, W., Optimal Three-layer Wireable Layouts,IEEE Transactions on Computers 33 (1984), 427–437.
Brown, D., and Rivest, R. L., New Lower Bounds on Channel Width,Proceedings of the CMU Conference on VLSI Systems and Computations, Computer Science Press, Rockville, MD, 1981, pp. 178–185.
Baker, B. S., Bhatt, S. N., and Leighton, T., An Approximation Algorithm for Manhattan Routing, in F. P. Preparata, ed.,Advances in Computing Research, Vol. 2, JAI Press, Greenwich, CT, 1984.
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Communicated by F. Thomson Leighton.
This work has been supported by “Consiglio Nazionale delle Ricerche” of Italy under a research grant.
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Lodi, E., Luccio, F. & Pagli, L. A preliminary study of a diagonal channel-routing model. Algorithmica 4, 585–597 (1989). https://doi.org/10.1007/BF01553910
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DOI: https://doi.org/10.1007/BF01553910